Gravity Exploration Generally
Gravity modeling is a method of geophysical exploration that uses measurements of variations in the earth's gravitational field to estimate properties of the earth's subsurface. The gravity of the earth has an average value of 9.8 m/s2, but it actually varies from 9.78 at the equator to 9.83 at the poles. Density variations of the earth's interior contribute to these gravity variations. Gravity exploration uses measurements of these gravity variations to study the interior of the earth.
The instrument used to measure gravity can be called a gravimeter or a gravity meter. An absolute gravimeter measures the absolute gravity value, for example, a value near 9.8 m/s2. A relative gravimeter measures relative gravity, for example, the difference between a gravity value at one location and a gravity value at a base station. Almost all modern relative gravimeters use a metal or quartz spring as a gravity measurement device. In exploration applications, we rarely use absolute gravimeters.
Gravity measurements can be acquired, using a relative gravimeter, on land, on the sea surface (from a moving marine vessel), on the seafloor, or in air (on a flying aircraft, or on a satellite). A land gravity survey is typically static: gravity meters remain at a location for minutes while taking readings, and then move to the next location. Each location is called a station. Ideally, the distribution of land survey stations will be regular. In contrast, marine and airborne gravity surveys are dynamic: measurements are taken along pre-defined vessel and flight lines. Data are sampled along these lines using a certain sampling rate (in time or distance). In a typical land survey, one or more gravimeters may be used. In a typical marine or airborne survey, generally, only one gravimeter is used. The locations of land stations and line samplings may be defined by (X, Y, Z) coordinates, and these coordinates are routinely determined by GPS. Gravity readings and their (X, Y, Z) coordinates can be exported from a gravimeter system to a data storage device.
The variation in measured gravity values is attributable to a combination of many effects. For example, the measurement may be influenced by the gravitational attraction of the moon and the sun, or the drift effect due to an imperfection of the materials used to build a gravimeter. However, in gravity modeling, only the gravity effects due to density variations of the earth's interior are of interest. Thus, a systematic process is used to estimate or compute these unwanted effects and then remove them from the measured gravity. The remaining value is called a gravity anomaly.
Generally, the gravity unit of m/s2 is too big for exploration applications. Thus, typically mGal is used as the unit of the gravity anomaly, where 9.8 m/s2=980000 mGal. A typical peak-to-peak range of gravity anomalies in a gravity exploration project is about tens of mGal.
2D Gravity Modeling
Gravity modeling is one way to interpret gravity data. Interpretation is the process of delineating the subsurface structure and density distribution from observed gravity data. Gravity modeling typically includes building an initial subsurface structural (i.e., geometric) model that consists of layers and closed bodies, assigning initial density values to these layers and bodies, computing the gravity responses produced by the model, and then comparing the observed gravity anomaly and the calculated gravity responses. If the observed gravity anomaly and the computed gravity responses don't match, either the structural model, the density values, or both are edited. Subsequently, the calculated gravity responses are recalculated and again compared to the observed gravity anomaly. This process may be repeated so that the observed gravity and the calculated gravity match in, for example, a least squares sense. The end result is a final structural and density model that interprets the observed gravity reasonably well.
Gravity modeling may be called three dimensional (3D) gravity modeling if the observed gravity covers a surface and if a 3D subsurface model is built or used to interpret the observed gravity. Gravity modeling may be called two dimensional (2D) gravity modeling if observed gravity along a profile (or line or cross section) is used, or a 2D subsurface model is built or used to interpret the observed gravity. The present disclosure relates to 2D gravity modeling.
When observed gravity is used, the measurements are each associated to an (X, Y, Z) location along a profile. A profile can be a straight or curved line and may be selected in different ways. For example, a profile may connect several land stations together. Alternatively, a profile may include only one marine or airborne survey line. Further, a profile may be selected according to an anomaly pattern in a gridded result of station or line data. One principle for a proper selection is that a profile should be perpendicular to a major known geological strike direction. After selecting a profile, observed gravity values are extracted along the profile using interpolation. Further, a profile may use an existing seismic profile. A seismic profile may have associated observed gravity, or observed gravity may be extracted from a gridded result.
Assignment of initial density values may be based on density logging in wells, density values of rock or core samples, or knowledge about the lithology, for example, rock types of the layers and bodies. Common density values of many rocks are well known.
2D Gravity Modeling with Variable Densities
2D gravity modeling is conducted routinely on a desktop or laptop computer. Thus, efficient computational algorithms are desirable. However, current solutions for 2D gravity modeling with variable densities suffer from inefficient computational algorithms.
For example, one solution to 2D gravity modeling with variable densities is to derive a mathematical formula for the gravity effect of a 2D body with a polygonal cross-section and with variable densities. Formulae have been published for densities varying either horizontally or vertically, but only in a certain form (exponential or polynomial). Other algorithms can process densities varying in both horizontal and vertical direction, but the density contrast must be in a specific polynomial function, and a computation of the gravity effect not at the origin of the coordinate system requires either a coordinate transformation or a solution transformation. In short, the density function form is restrictive and the computation is cumbersome.
An indirect solution is to discretize the subsurface model into smaller bodies. Existing mathematical formulae may be used to compute the gravity effects of each small body, e.g., with a rectangular cross section, but these formulae are complex, involving, for example, logarithms, arctangents and square roots.
Thus, a more efficient computation of gravity responses is required. The present disclosure includes system and methods directed towards more efficient 2D gravity modeling.